We show that every Mori dream space of globally Fregular type is of Fano type. As an application, we give a characterization of varieties of Fano type in terms of the singularities of their Cox rings.
Abstract. The purpose of this paper is to study the geometry of images of morphisms from Mori dream spaces. First we prove that a variety which admits a surjective morphism from a Mori dream space is again a Mori dream space. Secondly we introduce a natural fan structure on the effective cone of Mori dream spaces. We show that it encodes the information of Zariski decompositions, which in turn is equivalent to the information of the variation of GIT quotients of their Cox rings. Finally we show that under a surjective morphism between Mori dream spaces, the fan of the target space coincides with the restriction of the fan of the source.
We show that the bounded derived category of coherent sheaves on a smooth projective curve except the projective line admits no non-trivial semi-orthogonal decompositions.
Motivated by [Bor] and [Mar], we show the equality ([X] − [Y ]) · [A 1 ] = 0 in the Grothendieck ring of varieties, where (X, Y ) is a pair of Calabi-Yau 3-folds cut out from the pair of Grassmannians of type G 2 .
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.